The principle of operation of Rogowski transducers is well known. Details of the design and operation of Rogowski transducers can be found for example in “Wide bandwidth Rogowski current transducers—Part 1: The Rogowski Coil” European Power Electronics Journal Vol 3 No 1 Mar. 1993 pp 51-59 by W F Ray & R M Davis and in “Wide bandwidth Rogowski current transducers—Part 2: The Integrator” European Power Electronics Journal Vol 3 No 2 Jun. 1993 pp 116-122, by W F Ray.
In general terms a Rogowski transducer comprises a Rogowski coil and an integrator. A Rogowski coil is an electrically conductive coil having a substantially uniform turns density of N (turns/m) wound on a structure referred to herein as a “former”. The former comprises a non-magnetic material, typically plastic, of cross sectional area A (m2), and the coil is arranged to form a closed loop. In order to measure the value of a current in an electrical conductor, the Rogowski coil is placed around the conductor in order to induce a voltage (E) therein and providing a transducer output signal indicative of the sensed current in the conductor.
FIG. 1 shows schematically a Rogowski transducer comprising a typical Rogowski coil for which the coil loop can be opened and closed (generally called a “clip-around” coil) and for which the coil cross-section is circular. This type of coil is very well known. In FIG. 1 the Rogowski transducer utilises a conventional Rogowski coil 11 wound on a plastic former having a circular cross-section. The coil winding has a fixed end 13 connected to an integrator 12 and a free end 14. The free end 14 is returned to the fixed end 13 using a wire 15 situated in a hole along the central axis of the former.
Provided the coil in FIG. 1 is of uniform turns density N (turns/m), each turn having the same cross sectional area A (m2), and the coil is arranged to form a closed loop surrounding the current I1 (Amps) to be measured, then the voltage E (V) induced in the coil is proportional to the rate of change of the measured current dI1/dt according to the equation
                    E        =                                            μ              ·              NA                        ⁢                                          d                ⁢                                                                  ⁢                                  I                  1                                                            d                ⁢                                                                  ⁢                t                                              =                      H            ⁢                                          d                ⁢                                                                  ⁢                                  I                  1                                                            d                ⁢                                                                  ⁢                t                                                                        (        1        )            where H=μ·NA is the coil sensitivity (Vs/Amp) and μ is the magnetic permeability of the former material (normally 4π·10−9 H/m).
The coil terminal voltage E1 is connected to an integrator such that the output voltage from the integrator Vout is given by
                              V          out                =                              1                          T              I                                ⁢                      ∫                                                            E                  1                                ·                d                            ⁢                                                          ⁢              t                                                          (        2        )            where T1 is the integrator time constant.
If the coil termination voltage E1 is assumed to be the same as the induced voltage E, the overall transducer output voltage Vout is instantaneously proportional to the measured current I1 according to the relationship
                              V          out                =                              H                          T              I                                ⁢                      I            1                                              (        3        )            
The current waveform is shown in FIG. 1 as being a square wave. As the skilled reader will appreciate, this is convenient for illustrating the basic operation of the Rogowski coil but in practice this waveform could be of any shape and/or could comprise discontinuous pulses. Furthermore the integrator could be of analogue or digital form, as is already well known.
In other forms, the integrator comprises an operational amplifier 21, an input resistor and a feedback capacitor in the known inverting configuration as shown in FIG. 2. An example of this is GB 2034487A.
FIG. 3 shows an alternative form of known Rogowski coil for which the coil loop is permanently closed (generally called a “fixed” coil) and for which the coil cross section is rectangular. This type of coil is described, for example, in “Rogowski Coil” Patent JP2001102230 Filed 29, Sep. 1999 Published 13, Apr. 2001, by O Akira & I Satoru.
For this type of coil a printed circuit board (PCB) is generally used for the coil former and each coil turn comprises printed circuit strips on the major surfaces of the board together with plated though-holes joining the strips so as to make coil turns as shown. The coil is connected to an integrator such as shown schematically in FIG. 1 and the principle of the current measurement is the same as defined by equations (1) to (3). Other arrangements of printed circuit Rogowski coils are known.
In FIG. 3 the former of the board comprises a non-conductive substrate made of epoxy resin that is preferably filled with stratified glass, or a ceramic material. A four layer PCB is used in FIG. 3, wherein the PCB has first 31, second 32, third 33 and fourth 34 surfaces as shown. Conductive strips are deposited or etched on the outer (first 31 and fourth 34) surfaces using known photo-resistive processes. These strips are connected by plated through holes 39 to form a helical coil which proceeds in a first direction around the substrate.
A return conductor 37, which extends in an opposite direction to the coil, is deposited on the inner (second 32 and third 33) surfaces. The coil and return conductor 37 are connected to provide a ‘go and return’ path to minimise the influence of conductors outside the Rogowski coil.
Current measurement using Rogowski coils according to known methods is prone to inaccuracy. For example, if a Rogowski coil is not uniform then the voltage induced in the coil E will vary depending on the position of the current I within the Rogowski coil loop. Furthermore, external currents outside the Rogowski coil loop may contribute to the induced voltage E, thereby causing a measurement error. For good accuracy it is therefore desirable that the turns density (N) and area (A) are uniform around the complete loop. Printed circuit coils of the type shown in FIG. 3 are particularly good in this respect and are therefore often used in applications where high accuracy is important.
Another source of inaccuracy in known Rogowski transducers is the arrangement by which a Rogowski coil is connected to its termination. In FIG. 3 the first 35 and second 36 ends of the printed circuit winding are shown. The inner printed circuit conductor 37 is connected to the first end 35 and runs within the coil turns in a circular path to a connection point 38 adjacent to the second end 36. The external connections to the coil are then made to the second end 36 and to the connection point 38. The reason for this arrangement is to minimise or eliminate induced voltages in the coil due to magnetic fields perpendicular to the plane of the coil loop as described for example in Machinable Rogowski Coil, Design and Calibration” IEEE Transactions on Instrumentation & Measurement, Vol 45 No 2 Apr. 1996 pp 511-515, by J D Rambos. There are other arrangements which achieve this aim such as having two windings, one inside the other, one providing a forward path for the coil and the other a return path.
Another known source of inaccuracy in Rogowski transducers is the error arising due to changes in the coil temperature. Measuring devices or instruments often need to operate in a hot environment which can have a heating effect on the measuring device or instrument. If the temperature of the coil increases then the former will expand. This results in both elongation of its length and enlargement of its cross-sectional area. The elongation has the effect of reducing the turns density N of the winding and hence reducing the coil sensitivity H, whereas the increase in cross-sectional area A increases the coil sensitivity H. For a given current I1, changes in coil sensitivity will cause changes in the output voltage Vout as specified by equation (3).
The precautions for minimising errors mentioned hereabove are known. In the case of error due to temperature change the principle means of eliminating such error is explained in GB 2034487 referred to above.
The change in sensitivity of a Rogowski coil when it is subject to thermal expansion can be represented by the linear relationshipH=H0(1+αHθ)  (4)where H0 is the nominal sensitivity at nominal ambient temperature (say 20° C.), θ is the temperature difference between the actual coil temperature and the 20° C. temperature threshold. and αH is the corresponding coil sensitivity temperature coefficient (° C.−1), which can be predefined for a particular Rogowski coil. For example, it can be obtained experimentally by heating the coil.
The temperature compensation described herein is particularly, though not exclusively, applicable to Rogowski transducers for which, when the coil temperature increases, the resulting increase in area A predominates over the decrease in turns density N, in which case the temperature coefficient αH is positive.
The temperature compensation for current measurement applies equally to cases of increasing and decreasing temperature. In the decreasing case, αH remains positive and the coil sensitivity will decrease for a decrease in temperature. That is, applying equation (4) to such a scenario; θ is negative and, for positive αH, H becomes less than H0.
The resistance R1 of the coil comprises the sum of the resistance of all its turns. This resistance R1 increases with temperature when the turns are made of copper wire (or copper strip in the case of a printed circuit coil) or other conducting material.
The coil resistance R1 increases linearly with temperature and can be represented by the relationshipR1=R10(1+αRθ)  (5)where R10 is the nominal resistance at 20° C., θ is the temperature difference between the actual coil temperature and the 20° C. temperature threshold and αR is the corresponding temperature coefficient (° C.−1) for the coil windings. The temperature coefficient for copper is αR=3.8 10−3° C.−1. To put this value in context, the temperature coefficient for a high quality resistor is typically 1.5 10−5° C.−1. By using a high quality resistor for the terminating impedance R2 it may be assumed that R2 is relatively constant and unaffected by temperature changes.
The time constant for the integrator shown in FIG. 2 is given by T1=(R1+R2)·C.
Hence from (3)
            V      out              I      1        =                              H          0                ⁡                  (                      1            +                                          α                H                            ⁢              θ                                )                                      (                                                    R                10                            ⁡                              (                                  1                  +                                                            α                      R                                        ⁢                    θ                                                  )                                      +                          R              2                                )                ·        C              =                            H          0                ⁡                  (                      1            +                                          α                H                            ⁢              θ                                )                                      (                                    R              10                        +                          R              2                        +                                          R                10                            ⁢                              α                R                                              )                ·        C            
Taking the nominal time constant value TB)=(R10+R2)·C
                                          V            out                                I            1                          =                                            H              0                        ⁡                          (                              1                +                                                      α                    H                                    ⁢                  θ                                            )                                                          T                              I                ⁢                                                                  ⁢                0                                      ⁢                          {                              1                +                                                      (                                                                  R                        10                                                                                              R                          10                                                +                                                  R                          2                                                                                      )                                    ⁢                                      α                    R                                    ⁢                  θ                                            }                                                          (        6        )            
Thus by choosing R2 such that
                                          (                                          R                10                                                              R                  10                                +                                  R                  2                                                      )                    ·                      α            R                          =                  α          H                                    (        7        )            the effect of temperature θ can be eliminated and
            V      out              I      1        =            H      0              T      10      for all values of θ.
GB 2034487 envisages an arrangement “to achieve a high accuracy over a wide frequency band extending in particular to very low frequencies”. However the arrangement shown in GB 2034487 has an integrator circuit without any low frequency limit as shown in FIG. 2. Such an arrangement would suffer from very significant low frequency noise and drift. Practical integrators require a low frequency limit by placing something in parallel with the integrating capacitor such as a filter network as explained in “Wide bandwidth Rogowski current transducers—Part 2: The Integrator” European Power Electronics Journal Vol 3 No 2 Jun. 1993 pp 116-122, by W F Ray.
GB 2034487 also does not teach how to achieve satisfactory performance at high frequencies of transducer output. For satisfactory performance it is necessary for the Rogowski coil to be adequately damped. Without any terminating resistance (eg with the coil open circuit) the transducer output is susceptible to sustained oscillations due to the inter-action of the coil inductance and capacitance.
An object of the embodiments disclosed herein is to provide temperature compensation at low frequencies and damping at higher frequencies of transducer output.
An invention is set out in the claims.
The frequency below which the terminating impedance provides correct temperature compensation and above which the terminating impedance provides correct damping is for convenience referred to as the threshold frequency fTH. Damping is only necessary at or around the natural frequency of the coil f0. Hence fTH should be arranged as high as possible to provide a wide frequency range over which temperature compensation is provided whilst subject to the requirement that fTH must be sufficiently less than f0 to enable satisfactory damping at f0.
According to an aspect a current measurement device is provided, said current measuring device comprising a conductive coil that is arranged to produce a voltage as a result of a current being measured by the device. The conductive coil has a temperature dependent coil sensitivity factor. The device further comprises a terminating impedance connected to the conductive coil, wherein the terminating impedance may take on a first value below a predetermined frequency threshold, wherein that first value is suitable for providing temperature compensated error cancellation, and may take on a second different value above the predetermined frequency threshold, wherein that second value is suitable for providing damping in the coil. The predetermined frequency threshold can be arranged to be higher than the maximum frequency of the current to be measured but lower than the natural or resonant frequency of the coil.
The terminating impedance also connects the conductive coil to an output circuit, for example an integrator, wherein that output circuit is arranged to produce an output voltage that is an analogue of the current being measured. The terminating impedance attenuates the voltage produced by the conductive coil by an attenuation factor which is temperature dependent. The first value of the terminating impedance is arranged so that when there is a temperature change in the conductive coil which causes a change in the coil sensitivity factor, the attenuation factor also changes in the same proportion so that the value of the output voltage produced by the device is substantially unchanged as a result of the temperature change.
The second value of the terminating impedance may be arranged to be substantially equal to the characteristic impedance of the coil.
The coil is preferably a Rogowski coil. The output circuit of the device preferably includes an integrator.
The Rogowski coil is preferably a printed circuit Rogowski coil. The connection of the coil to the terminating impedance may be by means of a cable.
The terminating impedance is preferably a resistor or behaves as a resistor for the range of frequencies for which current measurement is required.
According to an aspect of the disclosed embodiments the terminating impedance comprises a first resistor in series with the parallel combination of a second resistor and a capacitor where the first resistor is the terminating resistance value required for damping the coil and where the sum of the resistors gives the terminating resistance required for temperature compensation. The value of the capacitor is chosen to provide a suitable threshold frequency of the transducer output above which damping applies and below which temperature compensation applies.
Other combinations of resistors and capacitors may be used to provide terminating impedances which provide both temperature compensation and damping according to the invention.
Thus a sophisticated yet easy to implement means is provided for compensating for the effects of temperature change on a coil such as a Rogowski coil so that they do not compromise the accuracy of current measurement obtainable over an acceptable range of frequencies using a device comprising the coil, such as Rogowski transducer whilst at the same time ensuring that the coil is adequately damped at and around its natural frequency.